How can I can make a 2D Png image (a portrait) into a 3d rotating model?
The closest thing I can think of to do this is to use the image as plane add-on. First go to File>User preferences (or Ctrl +Alt + U) >Addons, then search for Import-export: images as planes under the community supported level.

In object mode press Shift + A>Mesh>Add image plane, then when your file browser opens, select the image you want to use. Tab into edit mode, and model the plane to your liking, then Tab back to object mode to apply a solidify modifier. From there on, just add any finishing touches you want, keyframe, and you're all set.